Variable-magnifying-power symmetrical lens system

ABSTRACT

The invention provides a lens system especially adapted for use with photocopying machines, phototypesetters, etc. whose magnifying power may be varied continuously within a range near the unity magnification for example between 0.7 and 1.4. The lens system comprises lenses and lens groups symmetrically arranged with respect to a center stop in such a manner that the outermost lenses (the front and rear lenses) and/or the lens next to the outermost lenses may be shifted toward and away from the stop while maintaining said symmetrical relation. In an embodiment, the magnification is unity when the overall length of the lens system is the longest while the magnification is greater or smaller than unit when the overall length is shorter than the longest one. Aberrations including chromatic aberration are well corrected.

United. States Paten n91 Mikami Filed: :AppL No; 69,814

' VARIABLE-MAGNIFYING-POWER SYNIMETRICAL LENS SYSTEM Assignee:

Foreign Application Priority Data Sept. 8, 1969 Japan ..44 70570 US. Cl. ..350/184, 350/187, 350/202, 350/214, 350/255, 355/58 Int. Cl. ..G02b 15/ 16 Field of Search ..,...1..... ..350/l84, 187, 214,

References Cited UNITED STATES PATENTS Walters ..350/184 Altman et a1...

Demaine Schade ..350/184 X Apr. 17, 1973 FOREIGN PATENTS OR APPLICATIONS 12/1969 Great Britain ..350/184 5/1969 Switzerland ..350 212 [57] ABSTRACT The invention provides a lens system especially adapted for use with photocopying machines, phototypesetters, etc. whose magnifying power may be varied continuously within a range near the unity magnification for example between 0.7 and 1.4. The lens system comprises lenses and lens groups symmetrically arranged with respect to a center stop in such a manner that the outermost lenses (the front and rear lenses) and/or the lens next to the outermost lenses may be shifted toward and away from the stop while maintaining said symmetrical relation. In an embodiment, the magnification is unity when the overall length of the lens system is the longest while the 'magnification is greater or smaller than unit when the overall length is shorter than the longest one. Aberrations including chromatic aberration are well corrected.

9 Claims, 23 Drawing Figures PATENTED APR 1 7191s SHEET 1 [IF 7 FIG.

FIG. 2

B du INVENTORQ NOBUNAO MIKAMI ATTORNEY PATENTEDAPR 1 H975 SHEET 2 OF 7 -5 o 5 ASTIGMATISM SPHERICA'L AB E RRATI ON FIG. 58

FIG. 5A

0.8 TIMES SPHERICAL AB -no ASTIGMATISM PATENTEDAPR I 7 I975 SHEET 3 BF 7 FIG.

FIG. 6A

0.9 TIMES SPHERICAL ABERRATION ASTIGMATISM FIG. 78

FIG. 7A

5 O 5 ASTIGMATISM -5 o 5 SPHERICAL ABERRATION PAIENTEU APR 1 7 ms SHEET t Of 7 FIG. 8A

l.l TIMES ASTIGMATISM SPHERICAL ABERRATION FIG. 9

FIG. 9A

ASITIGMATISM PATENTEU APR 1 7 I975 SHEET 5 OF 7 5 O 5 ASTIGMATISM IOA -5 o 5 SPHERICAL ABERRATION FIG.

FIG. IIB

FIG. HA

ASTIGMATISM SPHERICAL ABERRATION H5 H6 WW8 I di W w i L 9.

FIG. l2

FIG. I

SHEET 6 [IF 7 PATENTEBAPRIYIQYS l r W r PATENTEUAPR 1 7191s SHEET 7 OF 7 FIG. 85

I VARIABLE-MAGNIFYING-POWER SYMMETRICAL LENS SYSTEM BACKGROUND OF THE INVENTION the copying lens with photocopying machines, phototypesetters, etc.

In general, the magnification used in the photocopying machines, phototypesetters and the like is nearly unity and slightly larger or smaller than unity depending upon requirements. For example, when an original of size A-3 in Japan (297 X 420 mm) is copied upon a photosensitized paper of A4 in Japan (210 X 297 mm), the magnification or reduction is about 0.7. When an original-is copied on a photosensitive paper having the same size as that of the original, the magnification is unity, but the magnification :must be varied slightly when an effective area or the area to be copied of the original is smaller than its size because of the perforations formed for filing.

For this purpose, there have been employed various methods. For example, in a large phototypesetter, the magnification may be varied by varying the distance between an original to be copied and a photosensitive medium. However, a complex mechanism is required in order to displace the original and/or photosensitized medium plane at a right angle relative to the optical axis with a higher degree of precision, thus resulting in high cost. Some photocopying machines employ a few objectives having different focal lengths and mounted upon a revolving nosepiece or turret, but the magnifying power may be only varied in steps. That is, the magnification cannot be varied continuously to a desired one. Furthermore, the lenses must be mounted with a higher degree of accuracy and the operation is rather complex. I

There has been proposed a lens system for photocopying machines in order to vary its magnifying power within a very limited range near unity between about 0.95 and 1.05 by utilizing the depth of focus of the lens system. One distinctive defect is, however, that the magnifying power may be varied only in a very limited small range.

There have been used in practice relatively simple photocopying machines in which one or two reflecting mirrors are moved in the optical path while an original and photosensitive medium planes are held stationary. In the photocopying machines employing only one may be continuously varied within a range near the unity magnification by shifting its lens elements symmetrically with respect to a center stop and which is best suited for use with a photocopying machine of the character in which both of an original and photosensitive medium plane are held stationary.

It is a further object of the present invention to provide a lens system of the character described above whose optical aberrations are well corrected so that an object may be sharply imaged with the minimum distortion.

In brief, the present invention provides a lens system comprising a plurality of meniscus lenses and groups arranged with symmetrical relation with respect to a center stop in such a manner that the outermost lenses and/or the lenses next to the outermost lenses may be shifted toward and away from the center stop while maintaining the symmetrical relation with respect to the center stop, whereby the magnifying power may be varied continuously within a range near the unity magnification for example between 0.7 and 1.4.

The present invention will become more apparent from the following description of two preferred embodiments thereof taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a diagrammatic view for explanation of the principle of the present invention;

FIG. 2 is a diagrammatic view of the first embodiment of the present invention;

FIG. 3 is a diagrammatic view of the optical system of a photocopying machine employing a variable-magnifying-power lens system in accordance with the present invention;

FIGS. 4-A and B through FIGS. 11-A and B depict the spherical aberration and astigmatism curves of the lens system illustrated in FIG. 2 when its magnifying power is varied from 0.7 to 1.4;

FIG. 12 is a diagrammaticview of the second embodiment of the present invention;

FIG. 13 is a diagrammatic view of the third embodiment of the present invention;

FIG. 14 is a diagrammatic view of the fourth embodiment of the present invention; and

reflecting mirror, the center of the original or photosensitive medium plane is displaced and it is very difficult to move the large-sized reflecting mirror with a higher degree of accuracy. In the photocopying machines employing two reflecting mirrors, when the angle of view becomes greater than 40, they cannot be used in practice.

SUMMARY OF THE INVENTION It is therefore the primary object of the present invention to provide an improved lens system whose magnifying power may be continuously varied within a range near unity magnification.

It is another object of the present invention to provide a'copying lens system whose magnifying power FIG. 15 is an elevational view showing mechanical apparatus for simultaneously moving two symmetrical lens elements in opposite directions with respect to the central stop.

First the underlying principle of the present invention will be discussed with reference to FIG. 1. When a distance between an original 1 and an image plane 2 is S, the focal length f,, of a focussing lens 3 for given magnification M may be given by the following expression:

fM I (1) (The aberrations and the length of principal points of the focussing lens 3 are not taken into consideration.) The increment or decrement of the focal length A f is given by the following equation when the magnification is varied from unity to l/ Vi: Af A S- [M/(l M ]S x 0.007 S 0.03f, 2 From Eq. (2) it will be seen that when the focal length 1 for unity magnification is reduced by about 3 percent, the magnification M becomes 1 V2 z 0.7 orfi z 1.4. It would be considered simple to design a zoom lens, that is variable magnifying power lens, satisfying the above condition because the variation is focal length f is exceedingly smaller than that of a zoom lens for cameras, but it is not true for a copying lens because a desired resolving power must be maintained all over the image plane at any magnification with the least distortion and a sufficient aperture efficiency in order to illuminate the image plane uniformly. Thus, the design is extremely difficult.

1n the copying lens in accordance with the present invention, lens elements are arranged symmetrically with respect to a center or stop so that the distortion which is the most difficult aberration to be corrected in a variablem agnifying-power lens may be perfectlycori'ected. Because of the symmetrical lens system, the coma and .color magnification aberration may also be satisfactorily well corrected while the spherical aberration, the astigmatism and on-axis-chromatic aberration may be also corrected to the maximum. The resolving power higher than 8 lines/mm may be obtained all over the-image plane in the-magnification range from about FIG. 2 depicts one embodiment ,of a variable-magnifying-power lens in accordance with the present invention consisting of eight groups and elements arranged symmetrically with respect to a stop. It is seen that all of the lens groups are meniscus lenses whose concave surfaces are all directed toward the stop. The first lens L, is a positive lens; the second lens L a negative lens; the third lens L5 and fourth lens L, are cemente'd; and the fifth lens L,,, a positive lensL'The sixth, seventh, eighth, ninth and tenth lenses L,,, L-,, L L

and L and the'fifth to first lenses are symmetrical with respect to the stop respectively. The focal lengths of the first positive lens L, and tenth positive lens L, is between two and five times the compound focal length of the lens system and these lenses L, and L have the configuration such as meniscus lens whose concave surface is directed toward the stop so that the change of aberrations caused upon the displacement of these lenses L, and L, may be minimized. It should be noted that these lenses L, and L,,, remain symmetrical with respect to the'stop when they are displaced.'The lens system comprising the lenses L L is known in the art as the Orthometar lens. The design data are given below where r, radius of curvature of lens; d, thicknesses of the lensesv and the air gaps between them along the optical axis. N, index of refraction of the lens elements when dline of helium is used; and V, Abbe numbers of the lens elements when d-line of helium is used. (n being numbered from front to rear) The maximum aperture ratio= 1 8 Focal length 248 mm 258 mm Magnification 0.7 1.4

4 r =59.50 d,,=10.43 N,,= 1.58900 V, 48.6 r,.==95.76 d,= 8.43 r,,,= -95.76 d, 10.43 N,,=1.58900 V =48.6 r,,=59.5O d,,=4.l9 r =-44.58 d,, 2.38 N, 1.62374 V, 47.0 r,,= l50.04 d,;,=12.77 N,,= 1.67790 V,,=55.5 r, 56.40 (A 1.48 r,,,==-64.89 a',,= 3.29 N,=-1.53172 V,,=48.9 r, =96.68 d 4.8 21.4 r, 101.29 11, 6.58 N,,,= 1.53996 V,,,= 59.7 r,,,=-78.65

Magnification 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 d,=d,, 4.8 14.0 19.7 21.4 19.9 16.5 11.8 6.3 focal length 248.3 253.6 257.0 258.1 257.1 255.1 252.3 249.1 distance in object 553.8 512.6 476.5 447.4 423.9 404.8 389.4 377.4 space distance in image 374.2 397.0 421.7 447.4 474.0 502.8 524.6 547.6

space total length of 100.31l8.7 130.1 133.5 130.4 123.7 114.3 103.3 lens system The distance in object space is that between the first surface of the first lens L, and the original 1 while the distance in image space is that between the 18th sur face of the 10th lens and the image plane 2 along the optical axis of the system. For all magnifications, the distance between the original 1 and the image plane 2 was maintained 1028.3 mm (See FIG. 3). FIGS. 4-A and B through FIGS. 1l-A and B inclusive depict the spherical aberration and astigmatism curves for given magnification respectively. The aperture ratio is plotted as the ordinate in the spherical aberration curves while the height from the center 'of the original is plotted as the ordinate in the astigmatism curves. It was confirmed that the distortion was all within 0.1 percent for all magnification.

The'coefficients of the spherical aberration 1, coma ll, astigmatism 111, curvature of field 1V and distortion V for given magnification are given below:

Magnification 0.7, d, d,,, =4.8

1 11 111 IV V 1 45.58- 3.27 0.23 1.88 0.15 2 11.84 2.15 -0.39 1.46 033 3 13.54 2.47 0.45 1.51 0.35 4 -8 l .29 6.l6 0.46 2.26 0.20 5 124.86 7.58 0.46 3.03 0.21 6 6.14 1.34 0.29 0.05 0.07 7 l73.99 l4.l9 l.l5 3.64 0.39 8 90.50 11.65 1.50 2.63 0.53 9 6.33 2.27 0.81 1.63 0.88 10 10.09 3.28 l.06 1.63 0.87 11 104.99 13.02 1.61 2.63 O.52 12 192.|4 15.30 1.21 3.64 0.38 13 4.84 1.13 0.26 0.05 0.07 14 134.79 8.04 0.47 3.03 0.20 15 88.82 6.59 0.48 2.26 0.20 16 17.17 -2.97 0.51' 1.51 0.35 17 15.02 2.59 0.44 --1.46 0.33 18 49.76 3.50 0.24 1.88 0.l5 E 12.67 0.21 0.01 0.23 0.00

Magnification 0.8, d d 14.0

I I1 111 IV V 1 53.64 2.34 0.10 2.03 0.09 2 l4.33 2.13 0.31 l.58 0.28 3 16.58 2.87 0.49 1.63 0.37 4 -96.74 7.0l -0.50 2.44 0.21 5 148.26 8.61 0.50 3.27 0.21 6 6.90 1.47 0.31 0.06 0.07 7 -207.44 16.17 -1.26 3.93 0.40 8 108.86 13.36 1.64 2.84 0.55 9 8. 10 -2.74 0.92 1.76 0. 91 l0 l0.96 3.47 1.10 1.76 0.91 11 119.89 l4.37 1.72 2.84 0.54 12 22l.25 16.98 l.30 3.93 0.40 1.3 5.92 1.31 0.29 0.06 0.07 14 155.82 8.94 0.51 3.27 0.21

with respect to the stop, but it will be understood that the lenses L,,and Lg may be shifted symmetrically with respe'cttothe stop while the lenses L and L are held stationa'ryas shown in FIG. 12. Alternatively the lenses L Li, L, and L may be shifted symmetrically with respect to-the stop as shown in FIG. 13. In these cases it "is preferable that the diameter of the lenses L, and L.

are made greater. All of the lenses L, L have been as being completely symmetrical with respect to the stop,

but the objects of the present invention may be equally attained when these lenses are arranged nearly symmetrical with respect to the stop.

V Abbe numbers of the lens elements when d-line' of helium is used. 6 (n is numbered from front to rear.) The maximum' aperture ratio= 1 ll Focallength 248mm 258 mm Magnification 0.7 1.4

FIG.' ;15 shows'thelens assembly of FIG. 1, with the two outermost lens'esL and L mounted for simultaneous movement in opposite directions while maintaining their positions symmetrical with respect to the stop at center line 20 of the lens assembly.

Lens element L, is mounted in a ring 21 supported on a carriage.22 which is movable along one or more guides 23 by means of a lead screw 24. The lead screw 24 is journalled at its center in afixed support 25. The other'end of the lead screw threadedly engages a carriage 26 supporting a ring 27 which encircles the lens el ement L The two ends of the lead screw 24 are oppositely threaded, i.e. one has a left hand thread and the other a right hand thread. One end of the lead screw is provided with a crank 28 by means of which it may be rotated.

- It may be seen that rotation of the crank 28 drives the lens element L in one direction. Thus the two lens element L in the opposite direction. Thus the two lens elements L, and L maintain their symmetrical positions with respect to the stop or center throughout their range of movement.

' FIG. 14 shows the fourth embodiment of the present about two and five times the compound It should be understood that the mechanism for moving the lens elements L, and L simultaneously at equal speeds in opposite directions may take various forms other than the simple form shown in FIG. l5.by way of example.

A similar mechanism may be used to move thelens elements L, and L as in the lens assembly of FIG. 12. Alternatively, the lens elements L and L could be moved together and the lens elements L, and L could be moved together, as in FIG. 13.

What is claimed is:

1. A variable-magnifying-power lens system between stationary object and image planes and whose magnification may be continuously varied within a range near unity magnification comprising a plurality of lens elements arranged symmetrically with respect to a central stop in such a manner that at least one of the outermost lens elements oneach side of the central stop may be shifted while maintaining the symmetry of all lens elements with respectto said central stop, and in which the lens system may be shifted as a unit to compensate for changes in focal lengths brought about by shifting of said lens elements.

2. A lens system according to claim 1, in which the outermost lens elements may be shifted.

3. A lens system according to claim 1, in which the next-to-the-outermost lens elements may be shifted.

4. A lens system according to claim 1, in which the outermost and the next-to-the-outermost lens elements may be shifted.

5. A variable-magnifying-power lens system according to claim 1, inwhich the focal length of each of the two outermost lens elements of the system are between focal length of the lens system. i

6. A lens system according to claim 5, in whi ch said 7 two outermost lens elements are meniscus lenses whose concave surfaces are directed toward said central stop. 7. A lens system according to claim 6, in which there are ten lens elements in said system which are numbered consecutively from front to rear, those of the lens elements having concave surfaces are positioned so that such surfaces are directed toward the central stop.

8. A variable-magnifying-power lenssystem whose magnification may be continuously varied within a range near the unity magnification comprising I 10 lens elements arranged symmetrical with respect toa center stop and numbered consecutively from front to rear,

' the first and tenth lenses being the positive meniscus lenses which are shifted toward and away from said center stop while maintaining said symmetry with respect to said center stop,

the second and ninth lenses being the negative meniscus lenses, v the third and fourth lenses and the seventh and eighth lenses being biconvex and biconcave lenses respectively cemented together, I the fifth and. sixth lenses being the positive meniscus lenses, I the concave surfaces of all of said lenses and cemented lenses being directed toward to said center stop, 1 the'individual lenses having the following radii of curvature of the surfaces, the thicknesses and distance along the optical axis of lenses and air spaces, the indexes of refraction and Abbe numbers when d-line of helium is used with the maximum aperture ratio of 1 8, the focal between 240 mg and 258 mm and the magnification range between 0.7 and 1.4;'

vwhere x with a numerical subscript indicates the radius of curvature of a surface identified by the subscript, numbering the surfaces consecutively from front to rear, a plus radius indicates a surface convex toward the front while a minus radius indicates a surface concave toward the front,

d with a numerical subscript indicates the thickness of the individual lens and the air space between the adjacent lenses numbering from front to rear, N with a subscript indicates the index of refraction of the lens identified by thesubscript and V with a subscript indicates the Abbe number of th lens identified by the subscript.

9. A variable-magnifying-power lens system whose magnification may be continuously varied within a range near the unity magnification comprising r 67.1 r,= 75.254 d, l.7l-20.585

respectively cemented together,

the fifth and sixth lenses being the positive meniscus lenses, I

the concave surfaces of all of said lenses and cemented lenses being directed toward to said center stop.

the individual lenses having the following radii of curvature of the surfaces, the thicknesses and distance along the optical axis of lenses and air spaces, the indexes of refraction and Abbe numbers when d-line of helium is used with the maximum aperture ratio of 1 1 l, the focal length between 248 mm and 258 mm and the magnification range between 0.7 and 1.4

where r with a numerical subscript indicates the radius of curvature of a surface identified by the subscript, numbering the surfaces consecutively from front to rear, a plus radius indicates a surface convex toward the front while a minus radius indicates a surface concave toward the front,

d with a numerical subscript indicates the thickness of the individual lens and the air space between the adjacent lenses numbering from front to rear,

N with a subscript indicates the index of refraction of the lens identified by the subscript and V with a subscript indicates the Abbe number of the lens identified by the subscript. 

1. A variable-magnifying-power lens system between stationary object and image planes and whose magnification may be continuously varied within a range near unity magnification comprising a plurality of lens elements arranged symmetrically with respect to a central stop in such a manner that at least one of the outermost lens elements on each side of the central stop may be shifted while maintaining the symmetry of all lens elements with respect to said central stop, and in which the lens system may be shifted as a unit to compensate for changes in focal lengths brought about by shifting of said lens elements.
 2. A lens system according to claim 1, in which the outermost lens elements may be shifted.
 3. A lens system according to claim 1, in which the next-to-the-outermost lens elements may be shifted.
 4. A lens system according to claim 1, in which the outermost and the next-to-the-outermost lens elements may be shifted.
 5. A variable-magnifying-power lens system according to claim 1, in which the focal length of each of the two outermost lens elements of the system are between about two and five times the compound focal length of the lens system.
 6. A lens system according to claim 5, in which said two outermost lens elements are meniscus lenses whose concave surfaces are directed toward said central stop.
 7. A lens system according to claim 6, in which there are ten lens elements in said system which are numbered consecutively from front to rear, those of the lens elements having concave surfaces are positioned so that such surfaces are directed toward the central stop.
 8. A variable-magnifying-power lens system whose magnification may be continuously varied within a range near the unity magnification comprising 10 lens elements arranged symmetrical with respect to a center stop and numbered consecutively from front to rear, the first and tenth lenses being the positive meniscus lenses which are shifted toward and away from said center stop while maintaining said symmetry with respect to said center stop, the second and ninth lenses being the negative meniscus lenses, the third and fourth lenses and the seventh and eighth lenses being biconvex and biconcave lenses respectively cemented together, the fifth and sixth lenses being the positive meniscus lenses, the concave surfaces of all of said lenses and cemented lenses being directed toward to said center stop, the individual lenses having the following radii of curvature of the surfaces, the thicknesses and distance along the optical axis of lenses and air spaces, the indexes of refraction and Abbe numbers when d-line of helium is used with the maximum aperture ratio of 1 : 8, the focal between 240 mm and 258 mm and the magnification range between 0.7 and 1.4; r1 78.65 d1 6.58 N1 32 1.53996 V1 59.7 r2 101.29 d2 4.8- 21.4 r3 96.68 d3 3.29 N2 1.53172 V2 48.9 r4 64.89 d4 1.48 r5 56.40 d5 12.77 N3 1.67790 V3 55.5 r6 - 150.04 D6 2.38 N4 1.62374 V4 47.0 r7 44.58 D7 4.19 r8 59.50 d8 10.43 N5 1.58900 V5 48.6 r9 95.76 d9 8.43 r10 - 95.76 d10 10.43 N6 1.58900 V6 48.6 r11 - 59.50 d11 4.19 r12 - 44.58 d12 2.38 N7 1.62374 V7 47.0 r13 150.04 d13 12.77 N8 1.67790 V8 55.5 r14 - 56.40 d14 1.48 r15 - 64.89 d15 3.29 N9 1.53172 V9 48.9 r16 -96.68 d16 4.8-21.4 r17 - 101.19 d17 6.58 N10 1.53996 V10 59.7 r10 - 78.65 where x with a numerical subscript indicates the radius of curvature of a surface identified by the subscript, numbering the surfaces consecutively from front to rear, a plus radius indicates a surface convex toward the front while a minus radius indicates a surface concave toward the front, d with a numerical subscript indicates the thickness of the individual lens and the air space between the adjacent lenses numbering from front to rear, N with a subscript indicates the index of refraction of the lens identified by the subscript and V with a subscript indicates the Abbe number of the lens identified by The subscript.
 9. A variable-magnifying-power lens system whose magnification may be continuously varied within a range near the unity magnification comprising 10 lens elements arranged symmetrical with respect to a center stop and numbered consecutively from front to rear, the first and tenth lenses being the positive meniscus lenses which are shifted toward and away from said center stop while maintaining said symmetry with respect to said center atop, the second and ninth lenses being the negative meniscus lenses, the third and fourth lenses and the seventh and eighth lenses being biconvex and biconcave lenses respectively cemented together, the fifth and sixth lenses being the positive meniscus lenses, the concave surfaces of all of said lenses and cemented lenses being directed toward to said center stop. the individual lenses having the following radii of curvature of the surfaces, the thicknesses and distance along the optical axis of lenses and air spaces, the indexes of refraction and Abbe numbers when d-line of helium is used with the maximum aperture ratio of 1 : 11, the focal length between 248 mm and 258 mm and the magnification range between 0.7 and 1.4; r1 - 67.1 d1 4.63 r2 75.254 d2 1.71-20.585 N1 1.54625 V1 59.7 r3 85.9 d3 3.45 r4 69.173 d4 2.41 N2 1.53993 V2 48.9 r5 53.785 d5 8.94 r6 - 144.61 d6 2.63 N3 1.68641 V3 55.5 r7 42.326 d6 2.90 N4 1.63306 V4 47.0 r8 59.235 d8 5.29 r9 88.855 d9 6.62 N5 1.61725 V5 46.2 r10 - 88.855 d10 5.29 V6 46.2 r11 -59.259 d11 2.90 N6 1.61725 r12 - 42.326 d12 2.63 V7 47.0 r13 144.61 d13 8.94 N7 1.63306 V8 55.5 r14 - 53.785 d14 2.41 N8 1.68641 r15 - 69.173 d15 3.45 V9 48.9 r16 -85.9 d16 1.71-20.585 N9 1.53933 r17 - 75.254 d17 4.36 V10 59.7 r18 - 67.1 N10 1.54625 where r with a numerical subscript indicates the radius of curvature of a surface identified by the subscript, numbering the surfaces consecutively from front to rear, a plus radius indicates a surface convex toward the front while a minus radius indicates a surface concave toward the front, d with a numerical subscript indicates the thickness of the individual lens and the air space between the adjacent lenses numbering from front to rear, N with a subscript indicates the index of refraction of the lens identified by the subscript and V with a subscript indicates the Abbe number of the lens identified by the subscript. 